The deposition of particulate matter on filter fibers (a system of cylinders) in a laminar flow normal to their axes has been simulated by a new Lattice Boltzmann model for two-phase flows. In the model, gas dynamics is solved by the Lattice Boltzmann method, while the transport of solid particle is described by the cellular automation probabilistic approach, where solid particles are constrained to move only on the same regular nodes as the fluid particles and their motion probabilities to neighboring lattices depend on the combined effect of drag forces from fluid, Brownian diffusion, and other external forces. The Lattice Boltzmann two-phase flow model is allowed to quantitatively simulate the filtration process of fibrous assembly, including the steady capture efficiency and pressure drop during the filtration processes of clean fibers, the dynamic evolution of the branch cluster structure, capture efficiency and pressure drop along with particle loading. The detailed information on the particle trajectories and the dendrite structures (fractral dimension and porosity) are obtained. Our results are in good agreement with previous theoretical predictions and experimental observations. (C) 2012 Elsevier B.V. All rights reserved.